AP Physics 1 · Unit 8 · Fluids

Continuity Practice Problems

Connect pipe area and average speed with conserved volume flow, mass flow, and delivered volume.

12 questions6 conceptual · 6 calculation

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Simulation scene from the Continuity lesson. — A scene from the related lesson. Open the practice to work through the questions.

What you’ll practice

Use the right area, rate, and time interval

Relate pipe size to fluid speed

Apply A₁v₁ = A₂v₂ through restrictions. Square radius or diameter factors before comparing speeds, then invert the relationship to design an outlet and calculate its percentage diameter reduction.

Distinguish volume and mass flow

Calculate m³/s and L/s from area and speed, then use density to find kg/s or g/s. For many parallel channels, compare the main vessel with the combined downstream area.

Size a duct and time a collection

Find the area needed to deliver one room-volume of air in a specified interval. Integrate steady flow over time to predict collected volume, fill time, and delivered liquid mass.

A question from this set

What changes at a restriction?

An incompressible liquid flows steadily through a full pipe with no leaks. Section 2 has one quarter of section 1’s cross-sectional area. Which comparison is correct?

Section 2 has four times the speed and the same volume flow rate.
Section 2 has four times both the speed and volume flow rate.
Both sections have the same speed because the liquid is incompressible.

Try it in the practice set

The narrow section carries the same steady volume flow at a greater average speed.

Key ideas

Keep speed, volume flow, and mass flow separate

A smaller section raises speed while volume flow stays constant

In steady incompressible flow without leaks, the same volume crosses every section during the same interval. Narrowing a pipe changes the speed needed to carry that volume. It does not remove part of the flow.

A bundle uses the sum of its channel areas

Many small parallel channels can have a much larger combined area than the vessel feeding them. Divide total volume flow by that combined area to find the area-averaged speed.

See the physics

Track a parcel and measure delivered volume

After attempting a question, watch tracers pass through a changing pipe and compare section measurements. Follow a fixed-volume parcel as its length changes, record a timed air-delivery interval, or let a liquid collection stop at its target volume.

Use a hint for a starting point or open a worked solution to follow the reasoning. Your progress saves in this browser, so you can return to unfinished questions.

Ready for continuity?

Begin with a conceptual question, then work through the calculations.

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